It's the wrong question. People are deterministic, but that doesn't mean they're always predictable .
In some sense, it's trivially true: we're physical systems, so of course* we're deterministic. The underlying physics that govern how the subatomic particles that make up the atoms that make up the molecules that make up the brain, is pretty well established at this point -- so if someone wants to assert some kind of special exemption for human brains: "everything else in the observable universe obeys physical law, but this is different!" the burden of proof is going to be pretty damn high. And nobody has ever put forth anything like real evidence for such an exemption -- the fact that "we don't understand how the brain works" doesn't mean it doesn't work in some fundamentally knowable way.
However, that doesn't mean that brains are (at least with current or reasonably-foreseeable-future technology) "ultimately tractable" even in principle, much less that we have any way of getting inside brains to see what people are going to do in real time.
And the reason people care about whether people are "deterministic" or not is because we want to know how to influence them, and for what we should assign praise/blame etc., and there's a common hidden assumption that determinism removes our ability to do that in some way. But I think that assumption's false (you don't see determinists just throwing up their hands and declaring ethics don't matter). There's a massive amount of physical evidence for determinism and no evidence at all against -- I'm not sure how anyone with a science background could believe otherwise at this point.
* "Predictable" here means something like "predictable by other humans, including via reasonably foreseeable technology". If we're in a simulation, the simulator can, by construct, "predict" the whole thing.
For a good layman's introduction I would suggest, "QED The Strange Theory of Light and Matter", (1986) by Feynman. Hard ideas but clear prose. I like to read it every few years to remind myself of the fundamentals.
If conclusive evidence were found that human consciousness is fundamentally dependent on QM processes to function, that would be a Nobel Prize-worthy discovery. Aside from some minor papers exploring the topic, no such evidence has been found AFAIK.
So? Transistors used in modern computers directly depend on quantum effects (semiconductor physics was an outgrowth of QM) as well, yet we do not need to take into account QM when writing software or designing microprocessors.
In any event, positing some sort of "QM consciousness" does nothing to save the concept of free will. Where is the "free will" in a fundamentally random phenomenon? Whether one accepts determinism or not, the notion of free will is incoherent.People probably act in a mostly deterministic when there are rules constraining them: sports, board games, social environments, lines. Maybe we are deterministic on a neurotransmitter level. But there's little control over external stimuli.
"As computer programmers, our formative intellectual experience is working with deterministic systems that have been designed by other human beings. These can be very complex, but the complexity is not the kind we find in the natural world. It is ultimately always tractable. Find the right abstractions, and the puzzle box opens before you.
The feeling of competence, control and delight in discovering a clever twist that solves a difficult problem is what makes being a computer programmer sometimes enjoyable."
I recently asked a friend whether he thought people were deterministic. He didn't think so (I don't either.) What do you think?